Audience targeting missing in SharePoint 2010?
Audience Targeting will not be enabled on lists & libraries by default! You must turn it ON by going to List Settings >> Audience Targeting Settings >> Enable audience targeting to turn audience targeting ON in SharePoint 2010.

3. For Audience Targeting, We need "User Profile Service Application"! So make sure the user profile service application is provisioned and running. Check the status of "User Profile Service" and "User Profile Synchronization Service" . Verify the UPSA is associated with your Web Application, by going to:

Central Administration >> Application Management

Manage Web Applications >> Highlight Your Web Application

Service Connections >> Make sure User Profile Service Application is checked.